====== Calc Spatial Lag ====== 

===== Description =====

This functor iteratively solves a spatial lag regression.

===== Inputs =====

^ Name  ^ Type  ^ Description  ^
| P Lag  | [[Real Value Type]]  | pLag is the autoregressive coefficient.   |
| W Neighborhoods  | [[Neighborhood Table Type]]  | The neighborhood matrix.  |
| X1  | [[Lookup Table Type]]  | x1 is the autoregressive term. When y is not known, x1 is used instead. In this case, a lookup table with same number of records and values equal to zero must be reported.  |
| B Coefficients  | [[Lookup Table Type]]  | Coefficients for independent variables x2, x3, x4... xn.  |
| E Error  | [[Real Value Type]]  | Regression random error term.  |

===== Output =====

^ Name               ^ Type                                  ^ Description                                 ^
| Y Result           | [[Lookup Table Type|Lookup Table  ]]  | A lookup table with Y results.              |
| Y Predicted Result | [[Lookup Table Type|Lookup Table  ]]  | A lookup table with the predicted results.  |

===== Group =====

[[Functor List#Statistics | Statistics]]

===== Notes =====

The lag spatial model is represented as follows:

<m>y = {rho W y}+{X beta}+ varepsilon</m>

where <m>rho</m> is the autoregressive coefficient; W is the spatial weight matrix; y is the dependent variable; X is co-variables' information matrix; <m>beta</m> is the regression coefficients and <m>varepsilon</m> is a random error term. W can be understood as the representation of the spatial interaction of a phenomenon. In a binary matrix, unit i is unit j’s neighbor if the spatial weight matrix cell, a<sub>ij</sub>, is equal to 1.

==== References ====

ANSELIN, L. SpaceStat TUTORIAL. Urbana-Champaign, University of Illinois, 1992.

ANSELIN, L. Spatial Externalities, Spatial Multipliers and Spatial Econometrics. Urbana-Champaign, University of Illinois, 2002.

===== Internal Name =====

CalcSpatialLag